For a CAT(0) cube complex , we
define a simplicial flag complex ,
called the simplicial boundary, which is a natural setting for studying nonhyperbolic behavior of
. We compare
to the Roller, visual
and Tits boundaries of ,
give conditions under which the natural CAT(1) metric on
makes it isometric to the Tits boundary, and prove a more general
statement relating the simplicial and Tits boundaries. The simplicial
boundary
allows us to interpolate between studying geodesic rays in
and the geometry
of its contact graph ,
which is known to be quasi-isometric to a tree, and we characterize
essential cube complexes for which the contact graph is bounded. Using
related techniques, we study divergence of combinatorial geodesics in
using
. Finally,
we rephrase the rank-rigidity theorem of Caprace and Sageev in terms of group actions
on
and
and state characterizations of cubulated groups with linear divergence in terms of
and .
